Find the Sum $$\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$$

question 208

Multiple Choice

Find the sum.
- $$\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$$

• A) \(- \frac { 1 } { 7 } \left( 1 - 3 ^ { n } \right)\)
• B) \(\frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)\)
• C) \(- \frac { 2 } { 7 } \left( 1 - 3 ^ { n } \right)\)
• D) \(- \frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)\)

---

Definitions:

Auto Repairs

Services aimed at fixing and maintaining vehicles for optimal performance.

Hours Per Day

A measure of time used to quantify the number of hours spent on an activity or activities within a 24-hour period.

Gasoline

A refined petroleum product used primarily as fuel in internal combustion engines.

Auto Repairs

Services conducted to fix or maintain vehicles to ensure they are in proper working condition, often necessitating parts replacement or maintenance.